Asked by cru
Express in simplest form: 36x−216x2−36 .(1 point)%0D%0AResponses%0D%0A%0D%0A36x−6%0D%0AStart Fraction 36 over x minus 6 End Fraction%0D%0A%0D%0A20x%0D%0AStart Fraction 20 over x End Fraction%0D%0A%0D%0A36x+6%0D%0AStart Fraction 36 over x plus 6 End Fraction%0D%0A%0D%0A6x
Answers
Answered by
GPT-4o mini
To simplify the expression \( 36x - 216x^2 - 36 \), we can factor it.
First, we can notice that each term can be divided by 36:
\[
36x - 216x^2 - 36 = 36(x - 6x^2 - 1)
\]
Next, we can reorder the terms inside the parentheses:
\[
36(-216x^2 + 36x - 36) = 36(-6(x^2 - 6x + 1))
\]
Now, we can factor the quadratic expression further if possible. However, this simplifies down incorrectly if we try further complexity, so we keep it straightforward. Simplifying can yield:
We can factor out the \( -6 \):
\[
-6(6x^2 - 6x + 6)
\]
However, this ultimately does not lead to any basic reduction on \( x \). Let’s return to the standard factorization where we see if we can take 36 out of \( x \) elements directly.
The correct simplification looks at common factors directly:
Factoring out \( -6 \) yields:
\[
= -6(6x^2 - 36x + 6)
\]
Final expression can give insight, but it’s still handled lightly, \( = 6(6x - 36)/x = \).
Thus, we can affirm that:
The expression is ultimately simplified to:
\[
27 + 6
\]
In simplest form, terms lead us to the factor directly on division evaluates into \( 6 \) as leading factors remain. Thus the easiest path reveals through:
The answer is thus \( 6x \).
First, we can notice that each term can be divided by 36:
\[
36x - 216x^2 - 36 = 36(x - 6x^2 - 1)
\]
Next, we can reorder the terms inside the parentheses:
\[
36(-216x^2 + 36x - 36) = 36(-6(x^2 - 6x + 1))
\]
Now, we can factor the quadratic expression further if possible. However, this simplifies down incorrectly if we try further complexity, so we keep it straightforward. Simplifying can yield:
We can factor out the \( -6 \):
\[
-6(6x^2 - 6x + 6)
\]
However, this ultimately does not lead to any basic reduction on \( x \). Let’s return to the standard factorization where we see if we can take 36 out of \( x \) elements directly.
The correct simplification looks at common factors directly:
Factoring out \( -6 \) yields:
\[
= -6(6x^2 - 36x + 6)
\]
Final expression can give insight, but it’s still handled lightly, \( = 6(6x - 36)/x = \).
Thus, we can affirm that:
The expression is ultimately simplified to:
\[
27 + 6
\]
In simplest form, terms lead us to the factor directly on division evaluates into \( 6 \) as leading factors remain. Thus the easiest path reveals through:
The answer is thus \( 6x \).
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